Luckaton Whitepaper
  • šŸ‘‹Welcome
  • ā°Presale and ICO
    • 🧱Staking During Presale
      • First Purchase - Buy and Stake
      • Claim & Stake During Presale
  • šŸ”“Tokenomics
    • šŸ“ˆLong-term growth strategy
  • šŸ¦Staking 101
    • šŸ“„Rules
    • šŸŖ›Staking dApp
      • Staking dApp Dashboard
      • Components
    • Staking & Betting
    • APY
    • STAKING $LUKT
    • Withdrawing From Staking
    • Claiming Rewards
  • ⚔Luckaton Game
    • šŸ§™Game Character
    • šŸ†Champions League
      • Luckaton Grand Finale
      • Champions
  • šŸ›£ļøRoadmap
    • Wall Of Luck
  • šŸ¤–Technicals
    • Technical Architecture
    • Randomization Framework
      • Games Smart Contracts
      • Random
    • Game Features
    • Betting
  • šŸ”¬Luckaton & Science
    • Luckaton Framework
    • Luck Index
    • Measurements
      • Rock-Paper-Scissors
      • Dice
      • Coin Flip
    • Researchers
  • šŸ’¬Marketing and Community
  • 🌻Conclusion
  • ā„¹ļøDisclaimer
  • šŸŒŽLuckaton Links
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On this page
  • Time-proof luck measuring tool
  • Expected Probability Calculation
  • Actual Outcome Analysis
  • Luck Index Calculation
  • Comparative Analysis
  • Interpretation
  1. Luckaton & Science
  2. Measurements

Dice

The most ancient game in the world with 5000+ years of history

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Last updated 1 year ago

Time-proof luck measuring tool

To scientifically justify the measurement of an individual's luck index through the outcomes of dice games, Luckaton uses structured approach that combines statistical analysis with probability theory. This method involves participants playing multiple rounds of dice games, allowing for a comparison of outcomes to determine deviations from expected results based on chance alone.

Expected Probability Calculation

For a fair six-sided dice, the expected probability (Pe​P_e​Pe​​) of any specific outcome (e.g., rolling a '6') in a single roll is 1/61/61/6 or approximately 0.167.

Actual Outcome Analysis

  • Calculate the actual frequency (Fa​F_a​Fa​​) of a specific outcome (e.g., '6') for each player over NNN rolls.

  • Determine the actual probability (Pa​P_a​Pa​​) of that outcome for each player as Pa​=Fa​/NP_a​=F_a​/NPa​​=Fa​​/N.

Luck Index Calculation

The (LILILI) for each player can be defined as the deviation of their actual probability from the expected probability, normalized by the expected probability, to account for the inherent variance in a game of chance:

LI=​Paā€‹āˆ’Pe​​PeLI=​\frac{P_aā€‹āˆ’P_e​​}{Pe}LI=​PePaā€‹ā€‹āˆ’Pe​​​​

This formula indicates how much more (or less) frequently an outcome occurs compared to what would be expected by chance, with positive values indicating greater than expected luck, and negative values indicating less.

Comparative Analysis

  • Compare the LILILI across all participants to assess individual variations in luck*

*Luckaton uses statistical methods (e.g., t-tests, ANOVA) to determine if the differences in LILILI among participants are statistically significant.

Interpretation

Interpret the Luck Index values to identify individuals who consistently experience better (or worse) outcomes than expected by random chance.


By quantifying deviations from expected probabilities, with the Luck Index, Luckaton offers a mathematical representation of luck that can be analyzed and interpreted to gain insights into the role of chance in players experiences.

Investigate patterns or correlations that may emerge from the comparative analysis of LILILI values across different participants.

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Luck Index